premise is -p

-r -> p therefore -r, modus ponens

is this assumption correct?

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- Jun 30th 2010, 08:01 PMdunstamodus ponens
premise is -p

-r -> p therefore -r, modus ponens

is this assumption correct? - Jun 30th 2010, 08:06 PMJhevon
this is not using modus ponens, and it's not true anyway. Remember, $\displaystyle \neg R \implies P$ is the same as saying $\displaystyle \neg P \implies R$. Since $\displaystyle \neg P$ is true, $\displaystyle R$ follows by modus ponens, not $\displaystyle \neg R$

- Jun 30th 2010, 08:28 PMdunsta
thanks

how about

premise -q

-p or q, therefore p, disjunctive syllogism

if q is false then p must be true, otherwise the whole condition is false??

or is it,

if -q(i.e. q is false)

then -p must be true for -p or q.

??

so

premise -q

-p or q, therefore -p, disjunctive syllogism

?? - Jun 30th 2010, 10:26 PMJhevon
- Jun 30th 2010, 11:32 PMdunsta
thanks for the help

the question I am working on is:

-r --> p, (-p) or q, -s -->(-p)and (-r), (-p) and r --> (-s) or t, -q, therefore t.

So far I have

1: -p, -p or q therefore -p conjunctive syllogism

2: -p, -r --> p therefore r modus ponens

3: -p, r, therefore -p and r conjunctive addition

(the next 2 lines I am unsure of)

4: -p and r, -s --> (-p) and(-r) /*-p is true from 1. but r is true from 2, so -r is not true. therefore (-p) and(-r) is not true so - (-p) and(-r) = -(p or r) demorgans.??? I don't know where to go with this? */

therefore s, because -s --> (-p) and(-r) is false.

5: (-p) and r (from 3), -s is false, (-s) or t therefore t disjunctive syllogism

am I close to showing the argument is valid??

thanks for any input and help

so -s --> (-p) and(-r)